Lauda, the F1 legend and Mercedes team chairman, had said that German Rosberg made the outfit look "stupid" by leaving it with a top driver to replace in December.
However, Rosberg told German newspaper Die Zeit: "I don't understand what Niki was riding when he said that. He must have misunderstood something.
"If it had only been up to me, I would rather have waited until Christmas to announce my retirement, but I didn't want to do that to the team."
Rosberg said there is little room for pure selfishness in F1, adding: "But my life belongs to me."
He defended his decision to quit as champion, insisting that had he failed to achieve his career dream this year, he would have tried again in 2017.
"It was strange," he said. "The thought of quitting was motivating. At the same time I couldn't think about it too much, otherwise I would lose focus."
Yet he did reveal the extent of the stress he was under as he fought for the title this year, saying that "because of the pressure", he struggled even to sleep.
Referring to his battles since 2014 with Lewis Hamilton, Rosberg told Sport Bild: "Fighting Lewis in the same car and losing twice was horrible - disgusting. I had to fight back again and again. Beating him is just exhausting. It sucks a lot out of you physically but most of all mentally.
"I did mental training, started to meditate. In Japan, I met a zen master before the race. I raised everything to the next level.
"Last winter, I bought two go-karts and drove, drove, drove - as much as when I was 14 and fought for the karting world championship. And I analysed why Lewis beat me so often in fights and realised I had to take more risks. Now I have reached my goal. Sure, I could have gone on, trying to defend the title. But why?
"It's easy to want more, more, more, but you also have to be careful and not lose yourself as a person. For me there is nothing more than this title. I wanted it and I got it.
"I feel as though I have climbed Mount Everest, I'm standing on the top and no peak that I see is higher."
Rosberg clinched the drivers' championship five points ahead of Hamilton.